Question Number 186539 by test1234 last updated on 05/Feb/23
$$\left(\mathrm{1}\right)\int\left(\underset{{x}\rightarrow{x}+\mathrm{1}} {\mathrm{lim}}\frac{{x}^{{x}+\mathrm{2}} {x}^{\mathrm{2}+{x}^{\mathrm{2}} } }{\:\sqrt{{x}}}\right){dx}=? \\ $$$$\left(\mathrm{2}\right)\int\frac{\mathrm{2}+{x}\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{1}−\mathrm{2}{x}+\mathrm{cos}\:\mathrm{3}{x}}{dx}=? \\ $$$$\left(\mathrm{3}\right)\:\underset{{n}=\mathrm{5}} {\overset{\mathrm{4}{n}} {\sum}}\left(\mathrm{3}{n}+\mathrm{2}{n}\right)=? \\ $$